A265187 Nonnegative m for which 2*floor(m^2/11) = floor(2*m^2/11).

0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Author

Bruno Berselli, Dec 04 2015

Keywords

• nonn
• easy

Comments

Also, nonnegative m not congruent to 3 or 8 (mod 11).

Integers x >= 0 satisfying k*floor(x^2/11) = floor(k*x^2/11) with k >= 0:

k = 0, 1: x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... (A001477);

k = 2: x = 0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, ... (this sequence);

k = 3: x = 0, 1, 5, 6, 10, 11, 12, 16, 17, 21, 22, ... (A265188);

k = 4..10: x = 0, 1, 10, 11, 12, 21, 22, 23, 32, 33, ... (A112654);

k > 10: x = 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, ... (A008593).

Primes in sequence: 2, 5, 7, 11, 13, 17, 23, 29, 31, 37, 43, 53, 59, ...

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A008593, A112654, A265188.

Cf. similar sequences provided by 2*floor(m^2/h) = floor(2*m^2/h): A005843 (h=2), A001477 (h=3,4), A008854 (h=5), A047266 (h=6), A047299 (h=7), A042965 (h=8), A060464 (h=9), A237415 (h=10), this sequence (h=11), A047263 (h=12).

Programs

Magma

[n: n in [0..100] | 2*Floor(n^2/11) eq Floor(2*n^2/11)];

Mathematica

Select[Range[0, 100], 2 Floor[#^2/11] == Floor[2 #^2/11] &]
Select[Range[0, 100], ! MemberQ[{3, 8}, Mod[#, 11]] &]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7, 9, 10, 11}, 80]

PARI

is(n)=2*(n^2\11) == (2*n^2)\11 \\ Anders Hellström, Dec 05 2015

Sage

[n for n in (0..100) if 2*floor(n^2/11) == floor(2*n^2/11)]

Formula

G.f.: x^2*(1 + x + 2*x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + x^8)/((1 - x)^2*(1 + x + x^2)*(1 + x^3 + x^6)).

a(n) = a(n-1) + a(n-9) - a(n-10) for n>10.